{"paper":{"title":"Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Spectral filtering on the log-density Hessian counts only tangent directions to estimate local intrinsic dimension even when noise fills most of high-dimensional space.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Genki Osada","submitted_at":"2026-05-02T03:30:55Z","abstract_excerpt":"While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension D.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the log-density Hessian exhibits a clear spectral separation where large eigenvalues reliably correspond to noise-dominated normal directions and near-zero eigenvalues to the tangent space, and that a fixed or simple cutoff can be applied without losing signal or introducing bias.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LHSD uses spectral filtering on the log-density Hessian to isolate tangent directions from noise and estimate local intrinsic dimension scalably via Stochastic Lanczos Quadrature.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spectral filtering on the log-density Hessian counts only tangent directions to estimate local intrinsic dimension even when noise fills most of high-dimensional space.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"67a4acd3a96eddba98add11cb5e6959878fd0f3601a1ebb28438b3587b955470"},"source":{"id":"2605.01221","kind":"arxiv","version":2},"verdict":{"id":"d4554f45-abde-4905-b453-fbb6f68a0849","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T14:06:53.178279Z","strongest_claim":"We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension D.","one_line_summary":"LHSD uses spectral filtering on the log-density Hessian to isolate tangent directions from noise and estimate local intrinsic dimension scalably via Stochastic Lanczos Quadrature.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the log-density Hessian exhibits a clear spectral separation where large eigenvalues reliably correspond to noise-dominated normal directions and near-zero eigenvalues to the tangent space, and that a fixed or simple cutoff can be applied without losing signal or introducing bias.","pith_extraction_headline":"Spectral filtering on the log-density Hessian counts only tangent directions to estimate local intrinsic dimension even when noise fills most of high-dimensional space."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01221/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T18:36:38.660101Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:29:15.746858Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e21d451e4b114d82946817b282c1d913694d1a201ad9fccd2d1ccd9f14ba43fe"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}